German Patent Application No. DE 197 22 334 describes that, to perform a diagnostic on an exhaust gas analyzer probe which reacts sensitively to at least one exhaust-gas component, to utilize the rate of change with which the signal reacts to changes in the concentration of the exhaust-gas component. In so doing, in a recognized overrun phase of the internal combustion engine, the time until the probe signal reacts to the altered concentration of the exhaust-gas component is measured. A precise prediction of the probe signal to be anticipated is not readily possible based on the prevailing operating conditions such as the overrun phase of the internal combustion engine with fuel cutoff.